Simplify to lowest terms. $\dfrac{60}{96}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 60 and 96? $60 = 2\cdot2\cdot3\cdot5$ $96 = 2\cdot2\cdot2\cdot2\cdot2\cdot3$ $\mbox{GCD}(60, 96) = 2\cdot2\cdot3 = 12$ $\dfrac{60}{96} = \dfrac{5 \cdot 12}{ 8\cdot 12}$ $\hphantom{\dfrac{60}{96}} = \dfrac{5}{8} \cdot \dfrac{12}{12}$ $\hphantom{\dfrac{60}{96}} = \dfrac{5}{8} \cdot 1$ $\hphantom{\dfrac{60}{96}} = \dfrac{5}{8}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{60}{96}= \dfrac{2\cdot30}{2\cdot48}= \dfrac{2\cdot 2\cdot15}{2\cdot 2\cdot24}= \dfrac{2\cdot 2\cdot 3\cdot5}{2\cdot 2\cdot 3\cdot8}= \dfrac{5}{8}$